Question

Enter your answer in the provided box. A sample of an unknown gas effuses in 11.1 min. An equal volume of H2 in the same apparatus under the same conditions effuses in 2.42 min. What is the molar mass of the unknown gas

Answer 1

Answer: The molar mass of the unknown gas is 9 g/mol

Step-by-step explanation:

From Graham's law of effusion rates, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

`(rate_1)/(rate_2)=\sqrt{(M_2)/(M_1)}`

`rate=(volume)/(time)`

Rate is volume effused per unit time. Since, the volumes are same, the formula could be written as:

`(t_B)/(t_A)=\sqrt{(M_B)/(M_A)}`

Putting the values in the formula:

`(2.42min)/(11.1min)=\sqrt{(M_(H_2))/(M_A)}`

`(2.42min)/(11.1min)=\sqrt{(2)/(M_A)}`

Squaring both sides:

`(2)/(M_A)=0.218`

`M_A=9g/mol`

The molar mass of the unknown gas is 9 g/mol